Question

You find a zero coupon bond with a par value of $25,000 and 18 years to maturity. If the yield to maturity on this bond is 5.7 percent, what is the dollar price of the bond? Assume semiannual compounding periods. (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

Answer 1

Zero coupon bond are bonds which do not make interest payment and pays par value of bond at maturity. These are generally issued at discount and redeemed at par

Formula to calculate price of zero coupon bond

Price of zero coupon bond

Par value*(1/((1+r)^n))

r is the yield to maturity

n is number of payments

Calculation of price of zero coupon bond

Semi-annual yield

2.85%

5.7%/2

No of payments

36

18*2

Price of zero coupon bond

25000*(1/(1.0285^36))

Price of zero coupon bond

25000*0.363618

Price of zero coupon bond

$9,090.45

Thus, price of zero coupon bond would be $9,090.45